Discriminating fuzz-balls from BHs is a challenging endeavour [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}. Recently significant progress has been made in the analysis of BH and fuzz-ball perturbation theory relying on the remarkable connection with quantum Seiberg-Witten (SW) curves for \({\cal N}=2\)  SYM theories [11]}, [12]}, [13]}, [14]}, [15]}, [16]}. Unfortunately this approach requires separability and integrability of the relevant dynamics. Since most micro-state geometries only admit time translation isometry, little progress can be made in this direction unless one restricts one's attention onto very special classes of micro-states.
Circular profiles in the two-charge system stand out as a very convenient playground to test ideas and address long-standing issues [17]}, [18]}. Indeed both geodesic motion and wave equation are separable in this background and the study of Quasi Normal Modes (QNMs), absorption and tidal deformability can be tackled with renewed strength thanks to the availability of new powerful techniques borrowed from SYM.
